'Inside Llewyn Davis,' 4.5 stars

Llewyn Davis is a good-but-not-great folk singer knocking around New York in the winter of 1961, talented enough to make the scene but not to influence it.

He’s also selfish, unhappy and deeply irresponsible. “Inside Llewyn Davis” follows him for a week of his life.

Why would anyone want to make that journey? Because, in the hands of Joel and Ethan Coen, even a miserable character is worth following around, and Davis, played with great unhappiness by Oscar Isaac, is no exception. All the performances are good, and all are weird, yet at the same time genuine (no easy feat). And layered atop this unhappy existence is a thick coating of humor (an even tougher feat). That mix, of a skewed look at the world coupled with dark humor, puts us comfortably — if that’s the word — in Coen brothers territory.

It’s also a risky movie, no doubt, not just because it requires keeping up with an unlikable protagonist, but because the Coens don’t just hint at the music, as some films would, but give us full performances. In for a penny, in for a pound, you might say.

Go all in. This is one of the strangest yet most satisfying movie experiences of the year, one of those films in which you can’t really appreciate what you’ve seen until it’s over. You just have to trust that the trip is worth the trouble. And it is.

Llewyn Davis has enjoyed modest success as part of a duo but is now striking out on his own. The film opens with him singing “Hang Me, Oh Hang Me” to a small crowd in a small club. The week proceeds from there.

Along the way, he will lose his friends’ cat, strike out for (and strike out in) Chicago, offend and infuriate his sister, as well as another set of friends whose couch he crashes on for a while, among other misdeeds.

He runs up quite the score, in other words.

When Davis lands at the apartment of Jim (Justin Timberlake) and Jean (Carey Mulligan), she is surprisingly mean to him. We will find out why, of course. They also are singers, frequenting the same clubs, and Jim manages to get Davis a gig singing a novelty song with another singer called “Please Mr. Kennedy” that is insanely infectious. Naturally Davis signs away his royalties for a cash payment of $200. For a musician, he has a tin ear toward life.

Davis decides to go to Chicago, to try to impress Bud Grossman (F. Murray Abraham), in hopes of getting signed. The trip is surreal, as Llewyn hitches a ride with a junkie bluesman (John Goodman, in his dangerous mode) and his monosyllabic poet driver (Garrett Hedlund); it’s here that one suspects we are entering “Odyssey” territory.

Only Davis is no hero. He will begin his journey where he starts it, in a loop he may never break out of. Meanwhile, after he finishes his set, we hear another up-and-coming folk singer on stage, one who will enjoy far more success. (Guess who.)

Because of the music and the journey, some are comparing “Inside Llewyn Davis” to the more obviously “Odyssey”-inspired “O Brother Where Art Thou?” For me it was more reminiscent of “A Serious Man,” one of the Coens’ smaller examinations of misery and unhappiness, but a brilliant one. This film mines similar sensibilities, but it also is its own free-standing work, a movie that will stick with you long after you’ve seen it, and I don’t mean just the melodies.

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